完美和非完美两阶段排序集抽样下几类正态性检验的功效与AUC研究

Efficiency and AUCs of Tests for Normality Under Perfect and Imperfect Double Ranked Set Sampling Design

检验功效和ROC曲线下面积(AUC)是反映统计检验判别能力的重要工具.文章在简单随机抽样(SRS)、排序集抽样(RSS)和两阶段排序集抽样(DRSS)下研究了Cramer-vonMises检验、Kolmogorov-Smirnov检验、Kuiper检验、Anderson-D arling检验和Jarque-Bera检验这五种正态性检验在完美和非完美排序情况下的检验功效和AUC,并通过蒙特卡洛模拟给出了各正态性检验在不同备择假设情况下的功效值和AUC值.根据模拟结果可得到以下结论:无论是在完美还是非完美排序情况下,基于RSS和DRSS的五种正态性检验功效和AUC均显著高于基于SRS的正态性检验,且基于DRSS的正态性检验在大部分情况下具有最高的数值.

Power of test and area under receiver operating characteristic curve(AUC)are important tools to reflect the discrimination abilities of statistical tests.In this paper,we study the powers and AUCs of tests of five normality tests including Cramervon-Mises test,Kolmogorov-Smirnov test,Kuiper test,Anderson-Darling test and Jarque-Bera test based on simple random sampling(SRS),ranked set sampling(RSS)and double-ranked set sampling(DRSS)under perfect and imperfect ranking.Then the powers and AUCs of the tests against different alternative assumptions are given by Monte Carlo simulation.According to the simulation results,the following conclusions can be obtained:Whether under perfect ranking or under imperfect ranking,the powers and AUCs of five normality tests based on RSS and DRSS are significantly higher than those based on SRS,and the normality tests based on DRSS usually provide the highest powers in most cases.